Rubber-like materials (e.g., elastomer, foam) have been used in many parts of engineering structures in various industries (e.g., automotive, aerospace, building, etc.) for years. Rubber-like materials often exhibit chrono-rheological (rheological and aging) behavior. The magnitudes of the chrono-rheological property change with time, and are often large enough that they cannot be neglected.
With advance of the modern computer technologies, an engineering structure (e.g., car, airplane, etc.) is generally designed and improved using computer aided engineering analysis. In order to capture structure responses including the aging effect of rubber-like materials, a numerical representation of the material properties needs to be determined and then incorporated in the application module or software in the computer aided engineering analysis. One of the numerical representations is a material constitutive equation, which relates the material strain-stress or force-displacement relationship. Generally, this is done by conducting specimen test of the material of interest, and then correlating the test results into a particular constitutive equation. However, material constitutive equations for rubber-like materials used in prior art approaches are generally inappropriate. Some are based on the assumption of incompressible elastic properties or certain special cases (e.g., neo-Hookean, Mooney-Rivlin). Others, (e.g., the Ogden equation) may include incompressible and compressible material properties, but not aging effect.
Shortcomings of the prior art approaches creates a problem for simulating the behaviors of elastomeric foam (a compressible and viscoelastic material), which is used extensively in the automotive industry. In particular, one of the industry standards for designing an automobile is to ensure safety of vehicle occupant or occupants in an event of collision or car crash. To ensure satisfying such requirement, automotive manufacturers need to conduct physical crash test of prototype of each vehicle model. In some instances, multiple tests for difference scenarios are required. Not only is physical crash test expensive to conduct, it also has its own set of difficulties and challenges (e.g., measurability, accuracy, reliability, repeatability, etc.). Therefore, computer simulation of a crash event (i.e., computer aided engineering analysis) has been used extensively to replace or at least minimize numbers of the physical prototype crash test.
In a physical crash test, one or more crash dummies are placed in the vehicle to represent human occupant or occupants (i.e., driver or drive plus passenger) to study the safety requirement. Crash dummy is made of a number of parts (e.g., head, torso, limbs, etc.) generally using foam material. Since crash dummy is generally damaged in a physical crash test and repaired thereafter to be reused in another test, different parts of a crash dummy may contain different aged foam material. In order to more accurately simulate such situation (i.e., multiple aged foam materials within one crash dummy), the computer aided engineering application software needs to be able to compute structure responses with a material constitutive equation including aging effect. Therefore, it would be desirable to have improved methods and systems for enabling simulation of material aging effect of a chrono-rheological material in a finite element analysis.